Processing math: 100%
 

MaxWong

avatar
Nom d'utilisateurMaxWong
But9675
Membership
Stats
Questions 169
Réponses 3812

0
1549
3
avatar+9675 
MaxWong  13 janv. 2019
 #1
avatar+9675 
0

Lemma: If x+1x=2cosα, then xn+1xn=2cosnα

 

If you want to see the proof of this, go here. I have done the proof in a previous answer before.

 

Now, if we consider α=2π3 and n=99, using the formula directly gives

 

x99+1x99=2cos(2π399)=2

.
9 juil. 2020
 #3
avatar+9675 
+1
9 juil. 2020